Using a marriage certificate is best. You can get it from the NSW Registar of Birth, Death and Marriages in the city. Make a few photocopies and get a Justice of the Peace to certify the copies. Then send the copies to the relevant companies you need to change her name with.

Also her passport, if you do it within 12 months of being married you don't have to pay for another passport. If you do it after a year, you have to pay for another passport

but should have mentioned, that we got married overseas, so we have an overseas marriage certificate. We plan to have her name changed on her passport & medicare, first and then tackle the banks and our investments.